New design simulation for a high-altitude dual-balloon system to extend lifetime and improve floating performance

Sherif SALEH,Weiling HE

aAviation and Aerospace Science Division,Military Technical College,Cairo 11811,Egypt

bSchool of Astronautics,Beihang University,Beijing 100083,China

1.Introduction

Scientific balloons have revealed an important role in aerospace science.Development of this technology is considered a major target to improve the performance in different phases.Zero-and super-pressure balloons are two common kinds of scientific balloons.Both kinds can carry different payloads to high altitudes according to application purposes.Zero-Pressure Balloons(ZPB)are characterized by large volume,light weight,and simple construction.On the other hand,they have disadvantages of a short lifetime and altitude instability during daytime and nighttime at a floating level,in addition to the useless payload of ballast masses that compensate for a lack of altitude during nighttime.The advent of Super-Pressure Balloons(SPB)was a significant jump in this field owing to the ability to overcome the serious disadvantages of zero-pressure balloons.The concept is to keep the balloon volume as constant as possible depending on the highly positive differential pressure between the lift gas and the atmosphere.However,this concept faces other problems such as material efficiency;there should be a high strength to resist high stresses on the balloon film and light-weight film because of the limited gross mass system.Therefore,a new design that collects the allowable advantages in both kinds is the new target to get longer lifetime,higher payload weight,and better altitude stability avoiding complicated designs and difficulties in material challenges.

Kreider and Kreith1established a computer model to predict the vertical motion and thermal effect for ascending zero-pressure balloons.Farley2introduced comprehensive mathematical and geometrical models for spherical,zeropressure,and super-pressure balloon shapes.Kayhan and Hastaoglu3referred to a significant influence of temperature variation during daytime and nighttime on the altitude stability.Cathey Jr.4studied the absorptivity to emissivity ratios for different materials to get the most acceptable properties for balloon film.Rand5presented super-pressure balloons to prolong lifetime.Many experimental works and flight tests demonstrated that super pressure kept a balloon with a constant volume.In addition,it was considered the main reason that caused film stresses.Therefore,innovations in materials were very important to improve the strength to weight ratio.Pavey6demonstrated a comparison between zero-and super pressure balloon efficiencies.He concluded thats uper pressure balloons were characterized by altitude stability and long lifetime,but super-pressure balloons needed to develop the design,shape,manufacture,and materials to encounter high differential pressure on their film.Garde7aimed to extend the flight duration and get an almost constant altitude.Thermal analysis for a thin-balloon film pumpkin shape was investigated.The pumpkin shape revealed better results than spherical or zero-pressure balloon shapes.Keese8analyzed the stress distribution on the balloon film dependent on the balloon shape, film thickness,and load tapes.Meanwhile,the equilibrium equations of loads in the meridian and radial directions were studied.Said et al.9used a thin film of fabrics and composite materials in a balloon envelope to provide a relatively high strength to weight ratio.Consequently,better crack resistance,handling,seaming,and sealing were obtained compared to those of isotropic materials such as mylar and nylon.Smith et al.10aimed to increase the strength of balloon film dependent on material development as reinforced film and coated fabrics.Moreover,seaming technology was developed.Main goals were the ability to carry payloads for a hundred days.Simpson11innovated a new approach modifying zero pressure balloons to be over-pressurized zero-pressure balloons.The performance of the new balloon structure was improved.Lew and Grant12introduced an approach to control the lifting gas temperature in the daytime to decrease the temperature difference between daytime and nighttime.This approach stated using a curtain material which was characterized by low solar absorption and high infrared emissivity.This material aimed to increase flight duration and decrease or even eliminate ballasting in zero-pressure or overpressure zeropressure balloons.Voss and Smith13presented new different methods to control altitude and obtain better performance for a balloon in a floating area.These methods were air ballast,mechanical compression,and differential expansion.The differential expansion method has a lower cost and weight,a greater altitude,and a longer duration flight than those of others.Meanwhile,these methods avoided difficulties in material developments.

The summarized attempts and difficulties are the challenges in material developments to improve the strength to weight ratio.14–16Other problems are wrinkling17,complicated shapes and structures18–20,and partially deployment and S cleft.21The previous discussion provides a guide for the importance of wide research to get avenues for balloons’longer lifetime,higher altitudes,ability to carry heavier payloads,and better altitude stability.

This work aims mainly to reduce or eliminate these difficulties and improve balloon floating performances such as extending lifetime,exceeding payload capacity,and enhancing floating altitude stability during daytime and nighttime.Therefore,the present paper is concerned on three aspects:(A)establish a new design that achieves these goals,(B)explain theoretically this idea and present mathematically the integration between both kinds of balloons in ascending and floating altitudes,and(C)simulate this design to get predicted results that support successful future real flights.In brief,this work is an attempt to collect the bene fits in both zero-and superpressure balloons while avoiding the disadvantages as much as possible to serve future applications.

2.New design concept

2.1.Idea description

This idea was inspired by two items: firstly,altitude control in airships by charging and discharging to air;secondly,altitude control by dual-balloon systems to employ a super-pressure balloon as a floater allowing a zero-pressure balloon keep its floating altitude.

The main objective is keeping a constant volume for a zeropressure balloon at its floating altitude,meanwhile,keeping the differential pressure equal to zero.During daytime,zeropressure balloon film and lift gas are superheated and vent some of the lift gas mass out to keep the differential pressure equal to zero,and the maximum volume hasn’t been exceeded.In the present design,the zero-pressure balloon is not opened to air but conducted with a small super-pressure balloon that works as an auxiliary container to store extra lift gas mass in the zero-pressure balloon during daytime at floating altitude.At nighttime,the stored lift gas mass is discharged to the zero-pressure balloon to compensate for the lack in the balloon volume keeping it constant,which consequently,keeps altitude level stability.In addition,this design doesn’t need to use a ballast mass,so it saves a large mass for additional useful payload.Further,keeping the lift gas mass almost constant during daytime and nighttime supports longer lifetime.

The present design collects the advantages for both kinds of zero-and super-pressure balloons.It is characterized by(A)a light-weight zero-pressure balloon avoiding problems of material developments,(B)abandoning the ballast mass that occupies a useless mass in the payload,(C)a super-pressure balloon volume as a container to partially store a lift gas mass at the floating altitude not similar to complete excursion of superpressure balloons that need special design to improve the strength to weight ratio,(D)long lifetime and altitude stability,and(E)a super-pressure balloon that can be partially filled at launching by lift gas to compensate for the leakage of lift gas at the float level and increase the lifetime of the balloon system.

In the following section,the theoretical design is explained concerning on the auxiliary equipment that transports helium from/to the zero-pressure balloon.

2.2.Theoretical design concept

This design depends on automatic control for a compressor and a solenoid valve according to the charge or discharge direction.The volume and differential pressure of the zeropressure balloon are considered as the boundary conditions for this process as shown in Fig.1.

Firstly,the definitions of compressor and solenoid valve are brie fly introduced.A gas compressor is a mechanical tool that increases gas pressure transporting it through pipes.Moreover,a gas compressor reduces the gas volume because of the ability of gas compressibility.A solenoid valve is a reliable electromechanical tool that uses an electrical signal to turn on/off at certain condition allowing flow to pass from a place to another.A combination of these tools together aims to discharge/charge gas from/to the zero-pressure balloon if the volume exceeds/decreases the balloon maximum volume(design volume).At daytime,the compressor increases the gas flow pressure to fill the super-pressure balloon storing the venting gas out from the zero-pressure balloon during daytime.At nighttime,the volume of the zero-pressure balloon decreases.Therefore,the super-pressure balloon discharges gas again into the zeropressure balloon throughout the valve at this time.Fig.2 represents the arrangement of the electrical equipment that is used to turn the compressor on.The solenoid valve weight and the necessary power are negligible compared to those of the compressor system.Therefore,the following calculation is concerned on the compressor and its electrical feeding systems.

Secondly,mathematical relations for the integrated design concept are provided utilizing typical zero-pressure balloon data as shown in Section 6.

(1)Mechanical system requirements

Helium’s molecular weight,specific heat ratio,critical pressure,and critical temperature are 4.002,1.66,33.2 psi(1psi=6.895 kPa),and 5.1 K,respectively.

where˙m is the helium mass flow rate,n is the molar flow rate,MW is the helium molecular weight,W is the actual average power for the compressor and motor system,Wsis the average necessary power,and ΔH is the molar enthalpy change in helium between the inlet and the outlet as follows:

Superscript‘ig” refers to ideal gas,‘R” refers to the residual into the compressor,and HRis the residual in the compressor enthalpy between the inlet and the outlet.

where Cpis the heat capacity of helium,and T is the temperature.

where R is the universal gas constant,P is the pressure,Vmis the molar volume,and a and b are the constants in the Redlich-Kwong equation of state depending on the critical temperature and pressure for helium.22

The absolute suction pressure at the inlet is 457 Pa,and the absolute discharge pressure is 732 Pa.Therefore,the compression ratio is 1.6 (＜3,so a single-stage compressor is recommended).

The inlet temperature is 226 K,and the outlet temperature is calculated depending on the compression ratio as follows:

where α is the helium specific heat ratio.

Helium volume inside the balloon V=RT/P;then,inlet molar volume V1≈4.1 m3/mol and outlet molar volume V2≈3.1 m3/mol.

Hence,ΔHig≈964.4 J/mol,HR≈ 9.7 J/mol,and then

Therefore, the necessary average power is Ws=0.8×974=779 W and the efficiency is assumed to be about 85%.

W=779/0.85=916 W,that means the compressor needs an electrical system that provides about 916 W as shown in the next step.As an example,The 1.5 hp(1 hp=746 W)compressor and motor units may be selected simply to be weighted totally less than about 15 kg.

(2)Electrical system requirements

It consists mainly of battery sets and a solar cell panel.In the following,the brief data and rough calculations of the selected commercial specifications for battery sets and the solar panel are introduced.

Rechargeable batteries such as Li-ion cells can be used,if the total voltage for cells is 24 V,so the total required current is 38.17 A.Note that the cells discharge is only 50%to keep the lifetime of these cells for about 300 cycles as mentioned in commercial specifications.The total required capacity is 38.17 A·h.One cell has a nominal capacity of 2.1 A·h.

Herein,the necessary safe number of cells are about 36 cells that are conducted in series and parallel(for example,9 series cells and 4 parallel sets).The weight of one cell is about 46 g,so the total weight of cells is about 1.66 kg.

These batteries provide power to the compressor in the first day for about 40 min,and the remaining time can be exploited to recharge batteries.Therefore,the assumed time of recharging is about 10 h.

For this case,the required capacity for the solar panel is about 75.6 A·h,and for 50%discharging of batteries,the capacity becomes 37.8 A·h.Commercially,this battery specification has the maximum charging voltage of 4.2 V for one cell.Therefore,the required voltage for 4 parallel sets is about 16.8 V.

This means that the required power to feed and recharge these battery sets from a solar panel during 10 h per day is about 63.5 W.Therefore,a 500 W solar cell panel with about 17%efficiency is good enough by rough calculations to provide this system with necessary power.

The gross weight for the mechanical and electrical systems together does not exceed about 30 kg in the worst case.The purpose of the preceding calculations roughly demonstrates the capability of applying this system mathematically,noting that the applied system may be better in the gross weight to promote the total performance of the dual-balloon system.Herein,an important conclusion should be mentioned:the old design consumes about 196 kg of the ballast masses without a useful payload to survive aloft about 10 days;in contrast,the new design consumes less than 100 kg of super-pressure balloon film and about 30 kg of auxiliary equipment weights.The new design needs about 130 kg for the auxiliary systems(super-pressure container and mechanical and electrical systems)saving about 33%weight that can be exploited as a useful payload.Therefore,the new design enhances a higher useful payload than those of ordinary systems.The super pressure container is suggested to be away from the zeropressure balloon avoiding the effect of super-pressure balloon bursting if it suddenly occurs,leading to only smooth descending to lower-level altitudes.In the following section,the thermodynamic relations for zero-and super-pressure balloons are addressed.

3.Environment description

3.1.Atmospheric model

The atmospheric model is categorized by three parameters:pressure,temperature,and density.These parameters are calculated from sea level to 32 km altitude23as follows:

and the air density at a different altitude can be calculated from the ideal gas law as

where Pairis the atmospheric pressure,Rairis the specific gas constant of air,Tairis the air temperature,and z is the balloon altitude.

3.2.Solar elevation angle model

The elevation angle of sun radiation represents the angular height of the sun measured from the horizon.This angle changes during daytime depending on latitude and the arrangement of this day in the year.24The sun elevation angle αELVcan be found using the following formula:

where δ is the declination angle which depends on the day of the year,φ is the location latitude,and HRA is the hour angle.

where d is the day number of the year(for example,Jan 1st is d=1).

where LST is the local solar time,h.

3.3.Cloud cover model

Cloud cover in fluences solar model formulation according to a thickness of cloud in altitude;it is selected about 0.15 to 12

(1)The influence of cloud cover on the intensity of direct solar radiation is

where qsunis the intensity of sun radiation,Isun，zis the product of the intensity of sun radiation at this altitude Isunand atmospheric transmittance τatm,and CF is the cloud factor.

(2)The influence of cloud cover on the intensity of reflected radiation is

where Albedogroundand Albedocloudare the radiation reflection factors for earth ground and cloud,25respectively.

4.Governing equations of high-altitude balloon ascending

There are five differential equations that derive high-altitude zero-and super-pressure balloons in ascending and floating processes:change in the heat transfer of lift gas and balloon skin,changes in the lift gas mass and volume,change in the altitude,and change in the climbing rate.

4.1.Balloon geometry

Firstly,the shape of the balloon is assumed to be spherical;the pressure of lift gas is described as

Zero-and super-pressure balloons consider ΔP=0 during ascending and ΔP=Pair{f(1+ΔT/Tair)+ΔT/Tair}at floating altitude,when the volume of the super-pressure balloon exceeds the design volume,where ΔT is the differential temperature between lift gas air,respectively,and f is the free lift ratio.The balloons volume is expressed as

where mgas,Rgas,Tgas,and Pgasare the mass,specific gas constant,temperature in K,and pressure of the lift gas,respectively.The balloon’s diameter is

The surface area of balloons is

The top projected area is

4.2.Thermal models

The thermal models of stratospheric balloons should express on two systems:the balloon film and the innerlift gas temperatures.The heat transfers between air,balloon film,and inner lift gas are shown in Fig.3.The following subsections describe the heat transfer relationships of the balloon skin and inner lift gas.

4.2.1.Heat transfer on balloon film skins

There are several factors that transfer heat to balloon skins.These factors are external and internal convection between air,outer and inner balloon skins,direct and reflected sun radiation,Infrared Radiation(IR),and heat emissivity to the surrounding air.26The film temperature skin differential equation is

where cfilm,mfilm,and Qfilmare the specific heat capacity,mass,and heat of the balloon film,respectively.

where Qcon，extis the total external convection heat,QIR，intis the total internal infrared radiation,QIR，e&sis the earth and sky infrared radiation,Qsunis the total direct and reflected sun radiation,Qcon，intis the total internal convection heat,and QIR，emitis the heat emission of the balloon film.

4.2.1.1.External convection.External convection of an ascending balloon occurs between the air and the external balloon film.It depends on two kinds.25Firstly,free convection which transfers heat to skin from the warmer surrounding air.Secondly,forced convection is excited from the relative velocity between the air and the ascending balloon.The external free convection heat transfer coefficient is

where Nuair，freeand Kairare the Nusselt number of free convection and the thermal conductivity of the air,respectively,which are defined as

where Grairis Grashof number for air,μairis air dynamic viscosity,Prairis Prandtl number for air,and27

where g is the gravitational acceleration.

The external forced convection heat transfer coefficient is

where Nuair，forcedis the Nusselt number of forced convection of the air,which is

where Re=|vz|Dρa(bǔ)ir/μairis the Reynolds number,and vzis the relative vertical velocity between the surrounding air and the balloon.

Hence,the effective external convection heat transfer coefficient is the greatest value of free and forced convection.Therefore,the total heat of the external convection is

where HCexternalis the effective external convection coefficient.

4.2.1.2.Internal convection.Heat expands throughout the inner balloon film to lift gas losing temperature.The internal free convection heat transfer coefficient is

where Nugasand Kgasare the Nusselt number and the thermal conductivity of the gas,respectively.

Carlson and Horn25introduced the correlation and Nusselt numbers that avoid a delay in the lift gas temperature rise,which consequently,avoid a reduction in the balloon climbing rate.By applying different forms in the present simulation model,the selected form is the best.The Nusselt number of the gas is

Hence,the total heat of the internal convection is

4.2.1.3.Film radiation emissivity.The infrared emission of the balloon film can be classified into two parts as shown in Fig.3.The first part is the external thermal radiation emission from the balloon film to surrounding atmosphere as described in this subsection.The second part is the internal thermal radiation emission where the balloon film reabsorbs the reflected heat on the balloon inner skin as described in the following subsection.The balloon film emits heat radiation as follows27:

where εeffis the effective emissivity factor of the balloon film,and σ is Stephan-Boltzmann constant(5.67 × 10-8).

4.2.1.4.Film radiation absorbance.The infrared radiation of sky and earth emits heat to the balloon film.Furthermore,there exists a heat interchange between the lift gas and the inner balloon skin by the internal reflected infrared radiation(Section 4.2.1.3).The film radiation absorbance can be divided into two parts as follows25:

The thermal interchange of the film is

where εintis the interchange effective emissivity factor.

The effective infrared radiation absorbance of the film is

where TBBis the blackball radiation temperature in K.

4.2.1.5.Solar thermal radiation.The solar radiation model consists of direct and reflected(albedo)solar radiations.Direct solar radiation depends on different factors such as balloon altitude,sun elevation angle,air transmission,cloud appearance,sun declination angle,and balloon launching day.On the other hand,the earth and sky surfaces reflect sun radiation depending on the reflection factor and cloud forecast.2

The direct solar radiation on the balloon film is

where α is the balloon film absorption factor for the sun radiation,qsunis the net gain direct solar intensity,τ is the balloon film transmission factor for the sun radiation,and reffis the effective reflectivity factor of the balloon film.

The intensity of the sun radiation can be formulated as follows:

where Isun，zis the resultant solar intensity at a certain altitude,CF is the cloud factor(CF≈0.15 to 1),Isunis the total solar intensity,and τatmis the atmospheric transmittance,and

where Airmass is air mass ratio;e is the orbital eccentricity,and RAUis the mean orbital radius,while for Earth,e=0.016708,and RAU=1;MA is a mean anomaly,and MA ≈ 2π(d/365); TA is a true anomaly, andis the air pressure at the launch surface.

The effective balloon film reflectivity is reff=r+r2+r3+...,in which r is the balloon film reflectivity.

The reflected sun radiation is defined as follows:

where qalbedois the allowable albedo intensity,and View Factor is the balloon subjected surface area to the reflected radiation depending on the balloon view angle,which are defined by qalbedo=Albedo ·Isun·sin(αELV)

where Rearthis the radius of the earth(6371000 m),and Albedogroundand Albedocloudare the re flected radiation factors for earth ground and cloud,respectively.

Herein,the total solar heat can be expressed by a summation of the direct and re flected solar radiation at the time of sun appearance as follows:

4.2.2.Heat transfer on lift gas

A variation of the lift gas temperature causes its compression and expansion which in fluence seriously on the balloon buoyancy.The internal convection,direct and reflected sun radiation,infrared radiation,and heat emissivity to the inner balloon film are the heat sources for the balloon lift gas.25The differential equation of the lift gas temperature is

where γ is the heat capacity ratio,Cvis the specific heat of the lift gas at a constant volume,and Qgasis the inner lift gas heat transfer which is defined by

where Qsun，gasis the total solar thermal radiation,QIR，gasis the net infrared thermal radiation,Qcon，int，gasis the internal convection heat,and QIR，emit，gasis the infrared radiation emission of the lift gas.

Heat transfers from/to the lift gas according to the following relations:25

4.2.2.1.Internal convection.The internal free convection between the lift gas and the inner skin is

4.2.2.2.Lift gas radiation emissivity.The lift gas loses its temperature by adiabatic expansion to the balloon film.The total heat emission of the lift gas is

where εeff，gasis the effective gas emissivity factor.

4.2.2.3.Gas radiation absorbance.The interchange between the lift gas and the inner balloon film is

Infrared radiation from sky and earth is

Therefore,the total infrared thermal radiation is

4.2.2.4.Solar radiation model.The impact of solar radiation on the lift gas can be divided into direct solar radiation and reflected solar radiation as mentioned before in the thermal equations of the balloon film.The total heat of solar radiation is

where αeff，gasis the effective solar absorption factor of the balloon gas.

4.3.Lift gas mass differential equation

At floating altitude,the balloon volume is a maximum.The zero-pressure balloon continues ascending by its momentum and inertia.Herein the differential pressure grows up,and gas should leak gradually out to prevent a balloon explosion causing a reduction in the lift gas mass.This lift gas mass is stored in the super-pressure balloon increasing its differential pressure using a compressor.The differential equation of the lift gas mass is

The lift gas mass is vented partially to the super-pressure balloon during the daytime,and then the necessary amount of lift gas that deploys the zero-pressure balloon is provided again at nighttime using a solenoid valve to compensate for the lack of the volume because of a change in energy.This process supports the altitude stability of the zero-pressure balloon without throwing ballast masses out as in ordinary systems.

4.4.Dynamic model

The dynamic model represents the force that helps balloons to ascend such as the buoyant force and forces that resist it such as the gross weight and drag force.The buoyant force is the force that is responsible on balloon lifting overcoming the gravitational force due to the gross weight.This force is provided by lift gas inflation inside the balloon where the gas density is lighter than the air density.The drag force is the aerodynamic force that resists the balloon ascending depending on the balloon shape,volume,velocity,and drag coefficient.

The dynamic equation of motion27is

where mvirtualis the total balloon mass including the lift gas mass,in addition to the air virtual mass that represents load above the ascent balloon head,and mvirtual=mgross+mgas+Cvirtual·ρa(bǔ)ir·V,in which Cvirtualis the virtual mass coefficient,and Cvirtual≈0.5;2mgrossis the gross mass(payload+ film+ballast);CDis the drag coefficient.

4.5.Altitude differential equation

The differential equation of altitude depends on the relative vertical velocity as follows:

5.Modeling and simulation

MATLAB M- file program is used to simulate the integrated high altitude balloons model predicting its floating performance.This program consists of the main program and two subroutines.Firstly,the main program includes the built-in solver function (ode45) which is the fourth orders Runge-Kutta numerical method and the initial conditions such as lift gas mass,lift gas temperature,balloon film temperature,altitude,and velocity.Then,subroutines describe the ascending constant parameters and thermodynamic nonlinear ordinary differential equations as shown in Section 4.

6.Results and analysis

6.1.Model validation

THERMTRAJ NASA model was adopted to validate zeropressure balloons.28Moreover,real flight 586NT was used to validate the super-pressure balloon model.29These models represented high-altitude zero-and super-pressure balloons with design volumes of 66375 and 56790 m3to float at altitudes of 36.7 and 30.5 km carrying payloads of 196.82 and 295 kg,respectively.Zero-and super-pressure balloons gross masses were 381 and 821 kg and initial lift gas masses were 69.221 and 140 kg.They were launched at local time 11:35 and 7:18 am from Palestine,Texas on July 24,1980 and Ft.Sumner,New Mexico on June 22,2008,respectively.There was a ballast mass of 109 kg in the super-pressure balloon model to grow pressure up from 200 to 350 Pa at floating altitude.

Figs.4 and 5 represent the zero-and super-pressure balloon trajectories in the ascending and floating phases,respectively.Both simulations are close to other models.The discrepancy at some points belongs to a change in the ascending and descending velocities,which is influenced by several parameters such as the initial lift gas mass,wind velocity prediction,location,time,and atmospheric model parameters.In the desired floating altitude,the zero-pressure model throws the ballast mass out at nighttime to compensate for the lack in the altitude level,but the super-pressure model throws ballast out to achieve a higher floating level increasing the differential pressure.

6.2.Heat energy and stored lift gas effects on altitude stability

A variation in temperatures within day/night causes expansion or contraction of lift gas leading to a variation in the balloon volume,which consequently,influences floating level stability.In the present design,the major goal is keeping the volume constant,resulting in a stable altitude for the zero-pressure balloon in the typical real flight model of 167 N.28Therefore,the following results demonstrate the behavior of a new integrated system at floating altitude level,i.e.,the extra lift gas inside the zero-pressure balloon is vented out to the super pressure balloon container with a volume of 20000 m3during daytime,and inversely charged at nighttime.

Fig.6 shows the variation and response of the most significant parameters that affect the altitude stability at launching time 11:35 am for 25 h.As mentioned before,a change in the lift gas temperature causes a direct change in the zero pressure balloon volume.During daytime,the expanded lift gas in the zero-pressure balloon at floating altitude tends to increase the balloon volume more than the design volume,so the lift gas should be vented out as shown in Figs.6(a)–(c)to avoid bursting,noting that the super-pressure balloon is partially inflated at the launching position to decrease the necessary power at floating altitude.Herein,the vented lift gas is stored in the super-pressure balloon which can resist super pressure because of increasing the free lift as shown in Figs.6(d)and(e).At nighttime,the stored lift gas is charged into the zero-pressure balloon to compensate for the leak in the volume because of temperature reduction.Fig.6(b)shows an approximately constant volume during daytime and nighttime,achieving the goal of the new integrated system.

6.3.Altitude stability

Fig.7 simulates the ascending and floating processes of the new integrated system.The floating altitude level of the zero-pressure balloon is stable for 25 h compared to altitude stability in Fig.4.Additionally,it shows about a 2 km higher altitude than that of an ordinary balloon because of additional super-pressure balloon lifting force.Hence,an ordinary zeropressure balloon is promoted to achieve a better floating performance for a long time.On the other hand,the new integrated system avoids the difficulties and hazards of ordinary super-pressure balloons.

6.4.Ascending velocity

Fig.8 shows the velocity for the dual-balloon system during ascending.At floating altitude,the ascending velocity tends to be zero ensuring that the altitude is stable in this area.

By a comparison between the ordinary and new features of the balloon systems mission,results are summarized in Table 1.

Finally,the present design is a theoretical simulation to improve the ballooning system performance while avoiding the complexity and disadvantages of ordinary systems.Moreover,the hopes to achieve this design experimentally in the future are indispensable.

Table 1 Comparison between ordinary and newly designed balloon systems.

7.Conclusions

This paper presents thermal and dynamic simulations for an integrated dual-balloon system in high altitudes.Preliminary calculations of the integrated design are described.Nonlinear ordinary differential equations of ascending zero-and superpressure balloons are analyzed.It aims to improve the floating performance while avoiding the challenges that ordinary highaltitude balloons face.Conclusions of applying this new integrated system are summarized as follows:

(1)It achieves theoretically the capability of applying this system.

(2)It attains a higher floating altitude level and a lighter weight than those of ordinary balloons.

(3)It is demonstrated that the floating level is stable during daytime and nighttime.

(4)It extends the lifetime of an ordinary zero-pressure balloons by using the simple construction of a superpressure balloon.

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